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A First Course in Differential Equations for Scientists and Engineers

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Re: A First Course in Differential Equations for Scientists and Engineers

#31

Post by sampo »

kenjackson wrote: post #28
sampo wrote: post #12

Earlier quoted context omitted.

If you have some mathematical maturity (you can read notation, work to understand each equation, have the patience to pretty much understand each equation and each page, because later ideas are built on understanding the previous ideas first), you can self-study a lot of mathematics. But almost everyone (mathematicians, physicists, engineers) who has that maturity, has probably taken a first course in differential eq…

I had self-studied this and then later studied under a teacher as well. I think the thing that I found hardest in my self-study was (and unfortunately this is about 25 years ago so my recollection might be a bit off) that it seemed like there was a lot written on just two equations (the heat equation and the wave equation). I didn't get why is 50 pages dedicated to one equation. Up until that point it felt like Calcu…

Heat equation / diffusion equation (same thing): parabolic.

Wave equation: hyperbolic.

Laplace's equation: elliptic. Laplace's equation is the steady state (equilibrium) solution of heat equation when the boundary conditions (or anything) don't change in time.

Re: A First Course in Differential Equations for Scientists and Engineers

#32

Post by sampo »

graycat wrote: post #27
jamescostian wrote: post #9

Earlier quoted context omitted.

> I really don't think that such topics can be self-studied Can you explain this? What makes something extremely difficult to be studied without a teacher? (I took calc in high school and never took diff eq, so my knowledge in this specific domain is basically zero)

With calculus, you are already well into ordinary differential equations -- partial differential equations are different, but with calculus you have a good start on the basics of those, too. A simple ordinary differential equation is below where of course just from calculus y'(t) = d/dt y(t) and the equation is y'(t) = k y(t) ( b - y(t)) So, for the context: t is time, say, in seconds. y is some real valued function…

> I looked through it, saw lots of intricate stuff, but wondered just why I should dig into that. Since then I read a story about Rota about how, apparently, he felt much the same about the material

Ah yes, the classic rant by Rota. Entertaining read, and good perspective (10 pages). Apparently written in 1997.

https://web.williams.edu/Mathematics/lg5/Rota.pdf

Re: A First Course in Differential Equations for Scientists and Engineers

#33

Post by thanatropism »

schitzapplebits wrote: post #18
TomMckenny wrote: post #16

On a related note, how do you take notes for math subjects with their multiline integrals and sumation and subscripts, division etc? I'm very much attached to recording every thing in simple text editors. Is there a "Notepad" or "TextEdit" for mathematical notation?

Don’t. Pay attention, write down the things that aren’t in the text book. And then learn to read the text book. It’s a hugely valuable skill.

I'm easily distracted, particularly from internal digressions. Taking notes helps me hold on to the thread.

Re: A First Course in Differential Equations for Scientists and Engineers

#34

Post by orbitingpluto »

tanderson92 wrote: post #19
saagarjha wrote: post #11

Earlier quoted context omitted.

Ugh, I hated that book. It never went into any detail in its “solutions” and the whole thing seemed like a bag of tricks for solving whatever example they were currently showing. Plus I had to deal with the monstrosity that is WileyPLUS.

ODEs as taught in a first-course undergraduate course is precisely a bag of tricks.

That you will never use in real life.

The chapters are first, second, and higher order were all a bunch of useless tricks. Then they introduce you to series solutions, where it starts to feel useful, and then they hit you on the side of the head with useless transforms.

ODEs are taught the way they are taught out of tradition, a bad tradition.

Re: A First Course in Differential Equations for Scientists and Engineers

#35

Post by sizzzzlerz »

I took DiffEq as an EE undergrad and, to my surprise, aced the course. For some reason, the concepts just resonated with me unlike other math courses where I had to work to gain an understanding of the material. A few years later, after graduating, I was taking courses leading to an MSEE and Partial DiffEq was offered as an option that I took. Thinking it was going to be similar to regular DE, I was soon in way over my head. Totally different material and concepts. I did end up passing the course but I can honestly state that I don't think I deserved it.

Re: A First Course in Differential Equations for Scientists and Engineers

#36

Post by kenjackson »

sampo wrote: post #31
kenjackson wrote: post #28

Earlier quoted context omitted.

I had self-studied this and then later studied under a teacher as well. I think the thing that I found hardest in my self-study was (and unfortunately this is about 25 years ago so my recollection might be a bit off) that it seemed like there was a lot written on just two equations (the heat equation and the wave equation). I didn't get why is 50 pages dedicated to one equation. Up until that point it felt like Calcu…

Heat equation / diffusion equation (same thing): parabolic. Wave equation: hyperbolic. Laplace's equation: elliptic. Laplace's equation is the steady state (equilibrium) solution of heat equation when the boundary conditions (or anything) don't change in time.

Thanks. And yes, Laplace was the third one. I think even your simple categorization would have made things much simpler for me. Or maybe I was just an idiot as an undergrad. :-)

Re: A First Course in Differential Equations for Scientists and Engineers

#37

Post by spapas82 »

jamescostian wrote: post #9
spapas82 wrote: post #5

We used the Boyce and DiPrima book back when I was an electrical engineering student (Elementary Differential Equations and Boundary Value Problems https://www.amazon.com/Elementary-Differential-Equations-Bou... ). I remember it was an excellent book with many great examples and correlation with physics topics like mechanics, waves etc. Too bad our other mathematics books weren't at this high standard :/ Also, I real…

> I really don't think that such topics can be self-studied Can you explain this? What makes something extremely difficult to be studied without a teacher? (I took calc in high school and never took diff eq, so my knowledge in this specific domain is basically zero)

Diff. eq. is a difficult topic. Not only you need to have a good understanding of a lot of other mathematic topics (derivatives, integrals etc) to properly understand it since it builds upon those but you also need somebody to guide you on how to think when solving such problems (i.e you'll need to solve diff. eq. together with your teacher).

Re: A First Course in Differential Equations for Scientists and Engineers

#38

Post by tnecniv »

tanderson92 wrote: post #19
saagarjha wrote: post #11

Earlier quoted context omitted.

Ugh, I hated that book. It never went into any detail in its “solutions” and the whole thing seemed like a bag of tricks for solving whatever example they were currently showing. Plus I had to deal with the monstrosity that is WileyPLUS.

ODEs as taught in a first-course undergraduate course is precisely a bag of tricks.

Indeed, and lame ones at that. I've found the qualitative theory of ODEs infinitely more interesting and useful for working with real problems.

Re: A First Course in Differential Equations for Scientists and Engineers

#39

Post by twtw »

orbitingpluto wrote: post #34
tanderson92 wrote: post #19

Earlier quoted context omitted.

ODEs as taught in a first-course undergraduate course is precisely a bag of tricks.

That you will never use in real life. The chapters are first, second, and higher order were all a bunch of useless tricks. Then they introduce you to series solutions, where it starts to feel useful, and then they hit you on the side of the head with useless transforms. ODEs are taught the way they are taught out of tradition, a bad tradition.

Those useless transforms (are you referring to Laplace and friends?) are pretty useful in EE.

Re: A First Course in Differential Equations for Scientists and Engineers

#40

Post by tanderson92 »

twtw wrote: post #39
orbitingpluto wrote: post #34

Earlier quoted context omitted.

That you will never use in real life. The chapters are first, second, and higher order were all a bunch of useless tricks. Then they introduce you to series solutions, where it starts to feel useful, and then they hit you on the side of the head with useless transforms. ODEs are taught the way they are taught out of tradition, a bad tradition.

Those useless transforms (are you referring to Laplace and friends?) are pretty useful in EE.

Yep, the transforms and series solutions are actually the most important part of ODEs, not just in EE but also in PDEs.
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